Chapter 1: Numeration Systems and Alternate Bases; Elementary Education Theme: Counting, Adding and Subtracting

Introduction

You are reading this book because you want to be a teacher someday; or maybe you already are a teacher and are working on getting your credentials. That’s wonderful. Being a teacher is one of the most challenging, interesting, and fun jobs you can have. And sharing with children (and grown ups) a love of math — of numbers and patterns and logical thinking — is one of the most challenging and fun parts of that.

But maybe you don’t like math. Or you liked it once but then it got difficult or scary at some point and you stopped liking it. Then this textbook is for you! We will explore patterns, we will play games (as much as is possible within a textbook) and you will find yourself seeing the fun in math.

In this chapter, you will learn about ancient number systems and different bases as a window into how we think in our own base ten number system. Understanding base ten more deeply will allow you to see how to help children learn how to count and how to add and subtract. A counting game, called Bizz Buzz, will make the number patterns come alive.

You will also learn many ways of thinking about addition and subtraction so that you can more clearly understand the methods you will be teaching your own students. The method that the famous mathematician, Karl Gauss, used when he was a bored child in grade school will help you see some amazing patterns.

Sometimes, you will be confused about how to do something and why the mathematics works that way. We hope that you will learn to work through your confusion both by challenging yourself and by being kind to yourself, asking lots of questions and getting the support of your classmates and professor to keep working and thinking until you achieve deeper understanding. This will help you to see how to work with your own students in the future, being both supportive of them and challenging them.

Finally, we hope that you will come to understand that there are many ways to do even basic mathematics and that math is more fun when we are open to different methods and ideas.

Authors Dr. Kathleen Offenholley and Dr. Fatima Prioleau